A Concise Introduction to Pure Mathematics, Second Edition
A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.
The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.
What's New in the Second Edition:
The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.
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Preface jd 1 Sets and Proofs
n1 Roots and Rational Powers
Congruence of Integers
More on Congruence
Counting and Choosing
More on Sets
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2-cycle Algebra answer bijection called Cartesian product choose codes coefficients complex numbers congruence equation connected plane graph contradiction coprime countable critic Ivor Smallbrain cube roots cubic equation cycle notation cycle-shape decimal expressions deduce define DEFINITION Let digits divides divisible edges elements equal equivalence classes equivalence relation Euclidean algorithm Euler's formula example Exercises for Chapter Fermat's Little Theorem finite sets function Fundamental Theorem Hence inequality infinite set integers s,t Liebeck lower bound Mathematical Induction mathematics method Miller's test modulo multiple n'h roots number system odd permutations pairs pigeonhole Platonic solids polyhedron positive integer positive real number prime factorization prime numbers product of prime PROOF Let prove rational number real line real number remainder result root of unity sends sequence set consisting solution solve subsets Suppose symbol tions total number true upper bound vertex vertices words write